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中文摘要：
深入研究利用卫星重力梯度张量分量组合确定地球重力场模型的广义轮胎调和分析方法。利用球面到轮胎面上的映射关系，借助圆周上的B样条插值技术，建立轮胎面上Fourier分析与调和分析的关系，实现地球重力场的高精度、高效率的自洽调和分析，克服传统调和分析中平滑因子不精确等引起的误差。将轮胎调和分析方法拓展到广义轮胎调和分析方法。模拟试算结果表明，利用广义轮胎调和分析技术，能够运用卫星重力张量分量数据以较高的精度还原地球重力场，验证算法的有效性和实用性。
英文摘要：
A generalized torus spherical harmonic analysis method for the recovery of an Earth gravity field model using gravity observations up to the second order components of the disturbing gravity gradient tensor is studied. The relationship between harmonic analysis and Fourier analysis of torus is established according to mapping from a sphere, where the sphere is rotated by 180° to a torus, and using the B-spline interpolation technique. As a result, self-consistent harmonic analysis of the Earth＇s gravity field with high accuracy and efficiency is implemented, which eliminates errors caused by the choice of inexact smoothing and de-smoothing factor of conventional harmonic analysis. The degree and order alternating recursive formulae of a series of fixed integrats of spherical harmonics that arise in torus harmonic analysis are given, which shows stable recursion and enable fast and accurate conversion from the Fourier to the spherical spectrum of various functionals of the gravity field. Numerical results indicate that the recovery of an Earth gravity field model with higher accuracy can be attained using the torus harmonic analysis method than the spherical harmonic analysis method, which also demonstrates the method is effective and practical.
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